Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e3 + 5;
int n, m, k;
int a[maxn][maxn], c[maxn][maxn];
int ans, tmp, cnt;
int flag;
pair<int, int> stk[maxn];
int jud(int x, int y, int v) {
  for (register int i = (1); i <= (cnt); i++) {
    if (abs(stk[i].first - x) + abs(stk[i].second - y) < abs(v - i)) return 0;
  }
  return 1;
}
int main() {
  int T, cas = 1;
  scanf("%d", &n);
  int m = 1;
  cnt = 0;
  while (cnt < n) {
    for (register int i = (1); i <= (m); i++)
      if (!c[i][m] && jud(i, m, cnt + 1)) {
        c[i][m] = 1;
        stk[++cnt] = make_pair(i, m);
        if (cnt == n) break;
      }
    if (cnt == n) break;
    for (register int i = (1); i <= (m); i++)
      if (!c[m][i] && jud(m, i, cnt + 1)) {
        c[m][i] = 1;
        stk[++cnt] = make_pair(m, i);
        if (cnt == n) break;
      }
    if (cnt == n) break;
    m++;
  }
  printf("%d\n", m);
  for (register int i = (1); i <= (cnt); i++)
    printf("%d %d\n", stk[i].first, stk[i].second);
  return 0;
}